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Re: st: Chi-square test for Categorical Data Analysis


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: st: Chi-square test for Categorical Data Analysis
Date   Wed, 19 Sep 2007 23:58:48 -0500

At 01:05 PM 9/19/2007, Austin Nichols wrote:
David Radwin <radwin@berkeley.edu>:
Any technique may lead you astray, but the technique you describe is,
I suspect, demonstrably inferior to others.  The reference you cite
applies only to estimating the mean or median of an open-ended
category with a Pareto distribution, and its abstract says that "the
choice of method and the selection of a mean or median estimator for
the open-ended category midpoint have substantial effects on analyses
in which income is the dependent variable."

The -intreg- approach proposed by Maarten relies on some shaky
assumptions, but I expect it is far preferable to imputing the
midpoint of intervals and testing for a difference in means as if you
have real data.
I hate ordinal variables like this - and I think it is even worse when they are independent rather than dependent variables. You don't like to treat them as continuous, nor do you like to create a bunch of dummies. Mid-point scoring is popular and easy but still problematic.

One possibility is to consider scoring methods. See section 6.2 of Powers & Xie:

http://www.stata.com/bookstore/smcda.html

When the ordinal var is independent, Long & Freese outline how to test whether it can be treated as continuous. See especially pp. 421-422 of

http://www.stata.com/bookstore/regmodcdvs.html

In principle, I think the intreg command sounds great. I wish Long and Freese discussed it in their book. What worries me are the "shaky assumptions" Austin mentions, especially since I don't have a very good feel for how often these assumptions are likely to be violated and what the consequences are. My own mini-mini discussion of intreg can be found at

http://www.nd.edu/~rwilliam/stats3/intreg3.pdf




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Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
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EMAIL: Richard.A.Williams.5@ND.Edu
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